This paper addresses the design and discrete time implementation of nonlinear observers for the e... more This paper addresses the design and discrete time implementation of nonlinear observers for the estimation of position and attitude with application to Unmanned Air Vehicles. A continuous time nonlinear observer on SE(3) is derived, that uses inertial and ranges measurements. The estimation errors are shown to converge exponentially fast to the desired equilibrium points in the presence of bias in the rate gyros. An observer discrete time implementation is proposed that resorts to recent geometric numeric integration results suitable for solving ODEs on SO(3). Simulation results are presented to assess the performance of the continuous time observer and of the discrete time implementation. The estimation results in the presence of noise in the inertial and range measurements are also analyzed.
Proceedings of the 2010 American Control Conference, 2010
This paper presents an experimentally tested solution to the problem of estimating the attitude o... more This paper presents an experimentally tested solution to the problem of estimating the attitude of a rigid body using rate gyros and a pan and tilt camera. An exponential input-to-state stable pan and tilt control law is used to keep the visual features in the image plane. A multi-rate implementation of the nonlinear attitude observer that uses recent results in geometric numeric integration is proposed. Practical aspects, such as the computation of suitable observer feedback gains, are considered. Experimental results obtained with a high accuracy motion rate table demonstrate the high level of performance attained by the proposed solution.
IEEE Transactions on Control Systems Technology, 2019
This paper presents an integrated visual servoing solution to the problem of quadrotor attitude e... more This paper presents an integrated visual servoing solution to the problem of quadrotor attitude estimation and stabilization based solely on image feedback from a pan and tilt camera and biased rate gyros. The solution comprises a control law for the quadrotor position and attitude, a control law for the pan and tilt camera platform, and an estimator for the vehicle attitude, whose interconnection stabilizes the quadrotor in hover above certain terrain landmarks. Lateral-longitudinal stabilization is achieved with a nested saturation control law by feedback of the image measurements, estimated attitude, and corrected angular velocity measurements and the vehicle is stabilized vertically by means of image feedback. Resorting to the input-to-state stability properties of the controllers, the quadrotor's position and attitude are shown to converge to the desired equilibrium point and, in the end, the interconnected system's closed loop is proven robust to observer estimation errors. Additionally, the pan and tilt camera is actively actuated to keep the relevant features visible in the image field of view for most operating conditions. The robustness and performance
This paper addresses the problem of attitude and rate gyros bias estimation using Set-Valued Obse... more This paper addresses the problem of attitude and rate gyros bias estimation using Set-Valued Observers (SVOs). We propose a singularity-free solution that exploits rate gyros measurements and vector observations corrupted by bounded noise providing bounds on the attitude of the rigid body and on the bias of the rate gyros. The sensor readings are fused directly by the SVO, without intermediate attitude computation. By taking advantage of the powerful new multi-core processors it is possible to increase the estimator convergence rate without compromising the execution time. The feasibility of the technique is demonstrated in simulation.
Proceedings of the IEEE Conference on Decision and Control, 2009
In this paper we consider the problem of estimating the attitude of a rigid body equipped with a ... more In this paper we consider the problem of estimating the attitude of a rigid body equipped with a triad of rate gyros and a pan and tilt camera. The nonlinear attitude observer integrates angular velocity measurements from rate gyros, with images of a planar scene provided by the camera. By exploiting directly sensor information, i) a stabilizing feedback law is introduced and exponential convergence to the origin of the estimation errors is shown; ii) an active vision system is proposed that relies on an image-based exponentially input-tostate stable (ISS) control law for the camera pan and tilt angular rates to keep the features in the image plane. The discrete time implementation of the observer makes use of recent results in geometric numeric integration to preserve the rotation matrix properties. Simulated and experimental results demonstrate the effectiveness and applicability of the proposed solution.
Proceedings of the IEEE Conference on Decision and Control, 2011
An optimal Set-Valued Observer (SVO) for attitude estimation that merges rate gyro readings with ... more An optimal Set-Valued Observer (SVO) for attitude estimation that merges rate gyro readings with body frame vectorial observations is proposed. The observer provides singularity-free estimates and considers sensor readings corrupted by bounded (but unknown) measurement noise. The suggested solution is an alternative method to the ones available in the literature, with the guarantee that the state is inside the estimated set. Optimal estimates are obtained, provided that there is no uncertainty in the angular velocity measurements, whereas the case with noisy rate gyros measurements is addressed by resorting to a relaxation of the problem. The sensor readings are exploited directly in the observer, without intermediate attitude estimate computation. Moreover, the feasibility of the technique is demonstrated in simulation.
Proceedings of the IEEE Conference on Decision and Control, 2012
This paper addresses the problem of Fault Detection and Isolation (FDI) for navigation systems eq... more This paper addresses the problem of Fault Detection and Isolation (FDI) for navigation systems equipped with sensors providing inertial measurements and vector observations. Two strategies are proposed. The first one takes advantage of existing hardware redundancy, providing sufficient conditions for the isolation of faults. The second approach exploits the analytical redundancy between the angular velocity measurements and the vector observations, by resorting to Set-Valued Observers (SVOs). The behavior of both strategies are illustrated in simulation.
The problem of attitude and rate gyro bias estimation is addressed by resorting to measurements a... more The problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations. A Set-Valued Observer (SVO) is proposed that has no singularities and that, for any initial conditions, provides a bounding set with guarantees of containing the actual (unknown) rotation matrix. The sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias. Conditions for the boundedness of the estimated sets are established and implementation details are discussed. The feasibility of the technique is demonstrated in simulation.
52nd IEEE Conference on Decision and Control, 2013
Observer design for rigid body translational and rotational motion has important applications to ... more Observer design for rigid body translational and rotational motion has important applications to unmanned or manned vehicles operating in air, underwater, or in space. An observer design for pose and velocity estimation for threedimensional rigid body motion, in the framework of geometric mechanics, is presented here. Resorting to convenient defined Lyapunov function, a nonlinear observer on the Special Euclidean Group (SE(3)) is derived. This observer is based on the exponential coordinates, which are used to represent the group of rigid body motions. Exponential convergence of the estimation errors is shown and boundedness of the estimation error under bounded unmodeled torques and forces is established. Since exponential coordinates can describe uniquely almost the entire group of rigid body motions, the resulting observer design is almost globally exponentially convergent. The observer is then applied to the free dynamics of a rigid vehicle. Numerical simulation results are presented to show the performance of this observer, both in the absence and with unmodeled forces and torques.
IEEE Transactions on Control Systems Technology, 2013
We address the problem of attitude and rate gyros bias estimation based on inertial and range dat... more We address the problem of attitude and rate gyros bias estimation based on inertial and range data. Range measurements are obtained from beacons installed in an inertial frame and acoustic sensors fixed in the moving body reference frame. A nonlinear observer is proposed and its stability and performance properties are studied resorting to Lyapunov techniques. In the presence of constant bias on the rate gyro measurements, the attitude and bias estimates are shown to converge exponentially fast to the desired values inside an almost global region of attraction. For time-varying bias with bounded derivative, a local result of ultimate boundedness is provided. The performance of the proposed nonlinear observer is validated experimentally using a high accuracy calibration table, which provides ground truth signals for comparison with the resulting estimates.
Proceedings of the IEEE Conference on Decision and Control, 2012
This work proposes a cascaded architecture comprising a nonlinear attitude observer and a nonline... more This work proposes a cascaded architecture comprising a nonlinear attitude observer and a nonlinear controller for position and attitude stabilization of a quadrotor. The attitude estimates are obtained from rate gyros measurements, corrupted by bias, and image coordinates from a set of landmarks on the terrain, obtained by a controllable pan and tilt camera. Lateral-longitudinal stabilization is achieved with a nested saturation control law by feedback of the image measurements, estimated body attitude, and corrected rate gyros measurements. The vehicle is stabilized vertically using an additional vertical position sensor. Due to the input-tostate stability property of controller, the quadrotor position and attitude are shown to converge to the desired equilibrium point and the convergence is robust to the estimation errors. Additionally, the pan and tilt camera is actively actuated to keep the landmarks visible in the image sensor for most operating conditions. The performance of the proposed ensemble is illustrated with some simulation results.
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